When one base is added to another base
Answers
- First, divide the number by the base to get the remainder. ...
- Then repeat the process by dividing the quotient of step 1, by the new base. ...
- Repeat this process until your quotient becomes less than the base.
Base systems like binary and hexadecimal seem a bit strange at first. The key is understanding how different systems “tick over” like an odometer when they are full. Base 10, our decimal system, “ticks over” when it gets 10 items, creating a new digit. We wait 60 seconds before “ticking over” to a new minute. Hex and binary are similar, but tick over every 16 and 2 items, respectively.
One point to realize is you need enough digits to “fill up” until you hit the next number. Let me demonstrate.
If we want to roll the odometer over every 10, so to speak, we need symbols for numbers one through nine; we haven’t reached ten yet. Imagine numbers as ticking slowly upward – at what point do you flip over the next unit and start from nothing.
We use zero, the number that doesn’t exist. Zero is quite a concept, it’s a placeholder, a blank, a space, and a whole lot more. Suffice it to say, Zero is one of the great inventions of all time.
Zero allows us to have an empty placeholder, something the Romans didn’t have. Look how unwieldly their numbers are without it.
George Orwell’s famous novel “1984″ would be “MCMLXXXIV”! Rolls right off the tongue.